Natural geometric unit system and electron magnetic moment anomaly

. ​ – Consequences of implementation of the natural geometric unit system (the SG) based on the pre-2019 SI system, in which four fundamental physical constants undergo joint numerical and dimensional normalization to unity c = G ​ = k = h = 1, with only one base geometric unit ​ u equal to √|h · G/c​ 3​ | m, where the Newtonian gravitational constant ​ G ≈ 6.673 655 205 · 10​ -11 m​ 3​ /(kg · s​ 2​ )​ , ​ are further explored. In addition to the earlier hypothesized simple electron mass to charge ratio formula ​ m​ e = e/(2​ 9​ πα)​ , and formulas for stable quarks rest masses: quark u ​ m​ u = √(⅔) / (2​ 7​ π √(πα)) u​ , equivalent of 2.360 MeV/c​ 2 and quark d ​ m​ d = √(⅓)​ -1 / (2​ 7​ π √(πα)) u​ , equivalent of 5.007 MeV/c​ 2​ , a simple formula for electron magnetic moment anomaly is proposed ​ α/2π - (α/2π)​ 2 - 2​ 8​ (α/2π)​ 3 - 2​ 12​ (α/2π)​ 4 - 2​ 16​ (α/2π)​ 5 - 2​ 24​ (α/2π)​ 6 ≈ 0.001 159 652 180​ . The finding supports the research area of purely geometric modelling of the fundamental physical forces and their unification. It seems plausible, that in the SG, with use of half integer powers of 2, 3, π and α only, all the fundamental properties of stable matter and electromagnetic radiation could be described.

It is equivalent to adding the following dependencies between units that are assumed to be independent in the unmodified SI: a. s = √|c 5   Conceptualizing Aristotle's approach to space (spacetime) and matter, which he also attributed rightfully to Plato as argued by J.
Fritsche in [4]: "In Physics IV:2, Aristotle argues for private Space of a body as its form (209 b 1-6) and as its matter (209 b [6][7][8][9][10][11] to conclude that Plato maintains that χώρα, matter, and space are the same (209 b 11-17).", we can see the unit u as the base element of all there is.
With this mindset we can interpret the Planck constant h as a scaling factor for the base unit, that translates the unit to man made measurement units systems. Furthemore the constants c and G (plus the constant k, which is directly dependent on c) can be interpreted as conversion factors from the ideal geometric reality (measured in u) to the reality perceived by humans' (as well as other living beings') senses (measured in seconds, meters, kilograms, amperes, kelvins, candelas and/or coulombs, webers, joules etc.).
We can postulate then, that electron is a base excitation of spacetime with two defining properties. One of them being its electromagnetic action at rest (the product of its electric charge and own magnetic flux) e · 2Φ 0 = u 2 and the other one its excitation activity (the product of its rest mass and excitation/oscillation wavelength, or, in other words, the product of its rest action and the speed of light) m e · λ C = u 2 (in SG rest mass is directly equivalent to rest energy). This description is equivalent to the description derived from P. Dirac´s and E. Schrödinger´s works by J. Maruani [6]: "the internal structure of the electron should consist of a massless charge describing, at light velocity, a vibrating motion in a domain defined by the Compton wavelength, the measured rest mass being generated by this very internal motion".   Table 2. Also a simple formula for quark s fits the experimental data: m s =1 / ((1⁄ 3) 3 √1⁄ 3 2 6 √(2πα) 3 /α ) u, equivalent of 95.59 MeV/c 2 ; but since it is an unstable particle, one can expect that its decay rate should be reflected in its SG formula. The same applies to all the remaining (unstable) charged fermions. The relevant equations are yet to be proposed.
In the SG the Schwinger limit of electromagnetic field flux density becomes the limit for the scale of physical events. Expressed as the shortest electromagnetic wave wavelength limit it is -in the SI -ca 12 times smaller than the Planck length.
They look like a set of harmonic frequencies of the √(2πα) 'tone' of the base spacetime excitation. Giving also the earlier mentioned relation of the order of the base tone to the order of the speed of light in vacuum factor in the SI counterparts to the SG relations, one can speculate that the differences in the order of the harmonic frequency of the base spacetime tone effect in differences between observable qualities: mass and charge, charge and magnetic flux, particle and wave, matter and radiation. The higher the density of the electromagnetic flux, the perceivably 'more material' it becomes, but not continuously, only in steps, from one harmonic frequency threshold up to another.
Interestingly, one can also notice that in the SG measured electron magnetic moment µ e relates to Bohr magneton µ B as follows (1) µ e = -µ B (1 + |e| 2 -|e| 4 -2 8 |e| 6 -2 12 |e| 8 -2 16 |e| 10 -2 24 |e| 12 ), which relation is another indication of the existence of higher order harmonic excitations of the base spacetime tone: electron. Each order being of different perceived quality, that subsequently interact with each other.
The value agrees with <1 part per billion accuracy with CODATA 2018 recommended value of electron magnetic moment anomaly a e ≈ 0.001 159 652 181. The difference is 6 times larger than the error allowance estimated by CODATA. The value (2) is purely theoretical, assuming no external influence whatsoever on free electron, while the CODATA 2018 recommended value is based on the most precise scientific measurements, but performed on Earth, under not fully understood influence of the planet itself and its surrounding masses and spacetime irregularities as well as external electromagnetic fields on the experimental results.
Conclusions. -The consistent implementation of the natural geometric unit system (the SG) and interpretation of the formulas for base physical properties written in the system lead to two hypotheses that are directly verifiable experimentally. The hypothesized values of the Newtonian gravitational constant and the electron magnetic moment anomaly are consistent to the convincing degree of accuracy with the most contemporary interpretations of the experimental data. The postulated relations leading to the hypothesized values are built in the SG with use of half integer powers of 2, π and α only. It seems plausible also, as show proposed relations for stable quarks, that adding to the mix only half integer powers of 3, could be enough to describe in the SG all the fundamental properties of stable matter and electromagnetic radiation. ***